Jet engines work by ingesting oxygen from the air and combusting it with an onboard fuel source like kerosene. But, on planets like Jupiter, with an abundance of hydrogen, would it be possible to remove the onboard fuel source and ingest both oxygen and hydrogen, carrying no fuel at all? This is assuming that the plane would be able to withstand very high pressures, and if Jupiter doesn't have the right amount of oxygen, any other planets that have the right atmosphere to support it.
Jupiter has hydrogen, but not oxygen. So you would need to bring your own oxygen, and essentially have just replaced what you use as "fuel."
If the atmosphere was, by itself, flammable then a jet engine should work. For a brief period of time before you set the atmosphere on fire.
Atmospheres don't tend to be flammable, for what are pretty obvious reasons if you think about it.
To elaborate on the other answer, you don't actually need any fuel or oxidizer to run a jet engine. Jet engines are just a type of open-cycle heat engine where the atmosphere is the working fluid and thrust happens by expelling it as reaction mass. Usually this is implemented as a form of internal combustion engine— Fuel burns inside, that provides the heat, the exhaust shoots out the back, and you go forwards fastly, very speed.
But you can completely remove the fuel-burning step, and replace it with any equivalent source of heat, and it would still be a fully functional jet engine. Nuclear reactors have been tried— No oxygen-burning fuel at all, just a bundle of uranium that the air goes around. Or if you cut a transparent window out of the side of the combustion chamber, and you shone a strong enough laser into it, that could work too.
On Jupiter, you would indeed need to bring your own oxygen/oxidizer, and ingest hydrogen as fuel.